On the special values of automorphic \(L\)-functions
type: Item
instance of: scholarly article
title: On the special values of automorphic \(L\)-functions
zbMATH Open document ID: 1051.11025
author: Joachim Mahnkopf
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-08-20T00:00:00Z
review text: This paper concerns certain \(L\)-functions. The author studies the values of \(L(\pi \otimes \chi,0)\), where \(\pi\) is a cuspidal automorphic representation of \(\text{GL}_n(\mathbb{A}_{\mathbb{Q}})\) with non-vanishing cohomology and \(\chi\) is a character which is critical for \(\pi\). The author proves the rationality of values of \(L(\pi \otimes \chi,0)\), under a certain non-vanishing assumption, based on considerations of cohomology via automorphic forms and Eisenstein series.
reviewed by: Dubravka Ban
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 2093967
zbMATH Keywords: automorphic \(L\)-functions
zbMATH Keywords: cohomology
MaRDI profile type: Publication
full work available at URL: j.crma.2004.03.012
OpenAlex ID: W2032282512
cites work: \(p\)-adic \(L\)-functions for \(\text{GL}(2n)\)
cites work: Q3484924
cites work: Q5750940
cites work: Q3041289
cites work: On Euler Products and the Classification of Automorphic Forms II
cites work: Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen
cites work: Q4175663
DOI: 10.1016/J.CRMA.2004.03.012
description: scientific article; zbMATH DE number 2093967